Spin spherical harmonics
Encyclopedia
In quantum mechanics
, spin spherical harmonics are spinor
s that are eigenstates of the square of the angular momentum operator
, and so are the natural spinorial analog of vector spherical harmonics
.
They are given in matrix form by
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, spin spherical harmonics are spinor
Spinor
In mathematics and physics, in particular in the theory of the orthogonal groups , spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the space of spinors cannot be built up in a unique and natural way from spatial vectors...
s that are eigenstates of the square of the angular momentum operator
Angular momentum operator
In quantum mechanics, the angular momentum operator is an operator analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic physics and other quantum problems involving rotational symmetry...
, and so are the natural spinorial analog of vector spherical harmonics
Vector spherical harmonics
In mathematics, vector spherical harmonics are an extension of the scalar spherical harmonics for the use with vector fields.-Definition:Several conventions have been used to define the VSH.We follow that of Barrera et al....
.
They are given in matrix form by